Inverse dynamics of redundant manipulators using a minimum number of control forces

The number of the control actuators used by the inverse kinematics and dynamics algorithms that have been developed in the literature for generating redundant robot joint trajectories is equal to the number of the degrees of freedom of the manipulator. In this article, an inverse dynamics algorithm that performs the tasks using only a minimum number of actuators is proposed. The number of actuators is equal to the dimension of the task space, and the control forces are solved simultaneously with the corresponding system motion. It is shown that because all degrees of freedom are not actuated, the control forces may lose the ability to make an instantaneous effect on the end-effector acceleration at certain configurations, yielding the dynamical equation set of the system to be singular. The dynamical equations are modified in the neighborhood of the singular configurations by utilizing higher-order derivative information, so that the singularities in the numerical procedure are avoided. Asymptotically stable inverse dynamics closed-loop control in the presence of perturbations is also discussed. The algorithm is further generalized to closed chain manipulators. Three-link and two-link redundant planar manipulators are analyzed to illustrate the validity of the approach.